Mercurial > octave-nkf
annotate scripts/statistics/base/std.m @ 8977:f464119ec165
further simplify some stats funcs
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Fri, 13 Mar 2009 21:26:13 +0100 |
| parents | eb63fbe60fab |
| children | 1bf0ce0930be |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2005, 2006, 2007, 2008, |
| 2 ## 2009 John W. Eaton | |
| 3200 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3200 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3367 | 20 ## -*- texinfo -*- |
| 21 ## @deftypefn {Function File} {} std (@var{x}) | |
| 4844 | 22 ## @deftypefnx {Function File} {} std (@var{x}, @var{opt}) |
| 23 ## @deftypefnx {Function File} {} std (@var{x}, @var{opt}, @var{dim}) | |
| 3367 | 24 ## If @var{x} is a vector, compute the standard deviation of the elements |
| 25 ## of @var{x}. | |
| 26 ## @iftex | |
| 27 ## @tex | |
| 28 ## $$ | |
| 6754 | 29 ## {\rm std} (x) = \sigma (x) = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} |
| 3367 | 30 ## $$ |
| 6754 | 31 ## where $\bar{x}$ is the mean value of $x$. |
| 3367 | 32 ## @end tex |
| 33 ## @end iftex | |
| 6754 | 34 ## @ifnottex |
| 3426 | 35 ## |
| 3367 | 36 ## @example |
| 37 ## @group | |
| 38 ## std (x) = sqrt (sumsq (x - mean (x)) / (n - 1)) | |
| 39 ## @end group | |
| 40 ## @end example | |
| 6754 | 41 ## @end ifnottex |
| 3367 | 42 ## If @var{x} is a matrix, compute the standard deviation for |
| 43 ## each column and return them in a row vector. | |
| 4844 | 44 ## |
| 45 ## The argument @var{opt} determines the type of normalization to use. Valid values | |
| 46 ## are | |
| 47 ## | |
| 48 ## @table @asis | |
| 49 ## @item 0: | |
| 6754 | 50 ## normalizes with @math{N-1}, provides the square root of best unbiased estimator of |
| 4844 | 51 ## the variance [default] |
| 52 ## @item 1: | |
| 6754 | 53 ## normalizes with @math{N}, this provides the square root of the second moment around |
| 4844 | 54 ## the mean |
| 55 ## @end table | |
| 56 ## | |
| 57 ## The third argument @var{dim} determines the dimension along which the standard | |
| 58 ## deviation is calculated. | |
| 5642 | 59 ## @seealso{mean, median} |
| 3367 | 60 ## @end deftypefn |
| 3200 | 61 |
| 62 ## Author: jwe | |
| 63 | |
| 4844 | 64 function retval = std (a, opt, dim) |
| 3200 | 65 |
| 4844 | 66 if (nargin < 1 || nargin > 3) |
| 6046 | 67 print_usage (); |
| 4844 | 68 endif |
| 69 if nargin < 3 | |
| 6024 | 70 dim = find (size (a) > 1, 1); |
| 8507 | 71 if (isempty (dim)) |
| 72 dim = 1; | |
| 73 endif | |
| 4844 | 74 endif |
| 8507 | 75 if (nargin < 2 || isempty (opt)) |
| 4844 | 76 opt = 0; |
| 3200 | 77 endif |
| 78 | |
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8977
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
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79 n = size (a, dim); |
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f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
80 if (n == 1) |
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f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
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81 retval = zeros (sz); |
| 4844 | 82 elseif (numel (a) > 0) |
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8977
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
83 retval = sqrt (sumsq (center (a, dim), dim) / (n + opt - 1)); |
| 3200 | 84 else |
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8977
f464119ec165
further simplify some stats funcs
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
85 error ("std: x must not be empty"); |
| 3200 | 86 endif |
| 87 | |
| 88 endfunction | |
| 7411 | 89 |
| 90 %!test | |
| 91 %! x = ones (10, 2); | |
| 92 %! y = [1, 3]; | |
| 93 %! assert(std (x) == [0, 0] && abs (std (y) - sqrt (2)) < sqrt (eps)); | |
| 94 | |
| 95 %!error std (); | |
| 96 | |
| 97 %!error std (1, 2, 3, 4); | |
| 98 |